The Prime Minister said it was "frustrating" that publication had been delayed and that the public "wants to see the answers of the inquiry".
Sir John Chilcot's inquiry completed public hearings in 2011, but the release of its report is understood to have been held back by negotiations over the publication of private communications between Tony Blair, prime minister at the time of the 2003 conflict, and then-US president George Bush.
The House of Commons Public Administration Committee described the delay as very serious and its chairman, Bernard Jenkin, has written to the Cabinet Office demanding an explanation for the hold-up.
Mr Cameron told Sky News: "My understanding is they will be able to publish before the end of the year and I much hope they can deliver on that timetable.
"The public wants to see the answers of the inquiry and we shouldn't have to wait too much longer."
The report could prove difficult for Labour in the build-up to the 2015 general election, reviving the issue of Mr Blair's decision to take the country to war.
Mr Jenkin said he is ready to summon ministers, for questioning by his committee on the reason why the report has not yet been published.
In an interview for BBC2's Daily Politics, Mr Jenkin said: "It's very serious this report is at least four years overdue, so we've written to the minister to ask for an explanation as to why these delays have occurred, what is holding up the publication of the report and how these issues are going to be resolved."